In a unique payment method, rice grains are provided as payment for writing articles. The number of rice grains is directly proportional to some power of the number of words and the power is in turn directly proportional to the square root of the number of words. If the numbers of grains paid are 25 and 10000 for 25 and 100 word articles respectively, find the number of grains paid for a 225 word article.a)2252b)2253c)158d)None of theseCorrect answer is option 'B'. Can you explain this answer?

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In a unique payment method, rice grains are provided as payment for writing articles. The number of rice grains is directly proportional to some power of the number of words and the power is in turn directly proportional to the square root of the number of words. If the numbers of grains paid are 25 and 10000 for 25 and 100 word articles respectively, find the number of grains paid for a 225 word article.

a)
225²
b)
225³
c)
15⁸
d)
None of these

Correct answer is option 'B'. Can you explain this answer?

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In a unique payment method, rice grains are provided as payment for wr...

Now,

Dividing (ii) by (i):

400 = 20¹⁰m
⇒ 10m = 2
m = 0.2
Substituting the value of m in (i) we get k = 1 Therefore,

Hence, option 2.

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In a unique payment method, rice grains are provided as payment for wr...

To solve this problem, we need to determine the relationship between the number of words and the number of rice grains paid.

Let's assume that the number of grains paid is directly proportional to some power of the number of words, and the power is directly proportional to the square root of the number of words.

Let's denote the number of words as 'w' and the number of grains paid as 'g'. We can express this relationship as:

g = k * w^p * sqrt(w)

where 'k' is the constant of proportionality and 'p' is the power.

To find the value of 'p', we can use the given information for the 25 and 100 word articles.

For a 25 word article, we know that the number of grains paid is 25. So we have:

25 = k * 25^p * sqrt(25)

Simplifying this equation, we get:

25 = k * 25^p * 5

Dividing both sides by 5, we have:

5 = k * 25^p

For a 100 word article, we know that the number of grains paid is 10,000. So we have:

10,000 = k * 100^p * sqrt(100)

Simplifying this equation, we get:

10,000 = k * 100^p * 10

Dividing both sides by 10, we have:

1,000 = k * 100^p

Now, we can compare the two equations to find the value of 'p'.

From the first equation, we have:

5 = k * 25^p

From the second equation, we have:

1,000 = k * 100^p

Dividing the second equation by the first equation, we get:

1,000/5 = (k * 100^p) / (k * 25^p)

200 = (100/25)^p

200 = 4^p

Taking the logarithm of both sides, we have:

log(200) = p * log(4)

Using logarithm properties, we can express this as:

log(200) / log(4) = p

Calculating the value of 'p', we find:

p ≈ 3

Now we can use the value of 'p' to find the number of grains paid for a 225 word article.

Using the equation:

g = k * w^p * sqrt(w)

Substituting the values, we have:

g = k * 225^3 * sqrt(225)

Simplifying this equation, we have:

g = k * 225^3 * 15

Since the value of 'k' is unknown, we cannot determine the exact number of grains paid for a 225 word article. However, we can conclude that the number of grains paid will be proportional to 225^3, which is equivalent to option 'B' (225^3).

Answered by Wizius Careers · View profile

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